Second order of accuracy stable difference schemes for hyperbolic problems subject to nonlocal conditions with self-adjoint operator
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Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
Amer Inst Pyhsics
Abstract
In the present paper, two new second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value problem
{ d(2)u(t)/dt(2) + Au(t) = f(t) (0 <= t <= 1),
u(0) = Sigma(n)(j=1) alpha(j)u(lambda(j)) + phi, u(t)(0) = Sigma(n)(j=1) beta(j)u(t)(lambda(j)) + psi,
0 < lambda(1) < lambda(2) < ... < lambda(n) <= 1
for differential equations in a Hilbert space H with the self-adjoint positive definite operator A. The stability estimates for the solutions of these difference schemes are established. In practice, one-dimensional hyperbolic equation with nonlocal boundary conditions and multidimensional hyperbolic equation with Dirichlet conditions are considered. The stability estimates for the solutions of difference schemes for the nonlocal boundary value hyperbolic problems are obtained and the numerical results are presented to support our theoretical statements.
Description
Bu çalışma, 19-25 Eylül 2011 tarihleri arasında Halkidiki[Yunanistan]’da düzenlenen International Conference on Numerical Analysis and Applied Mathematics (ICNAAM)’da bildiri olarak sunulmuştur.
Keywords
Mathematics, Hyperbolic equation, Nonlocal boundary value problems, Stability, Boundary-value-problems, Parabolic equations
Citation
Ashyralyev, A. vd. (2011). "Second order of accuracy stable difference schemes for hyperbolic problems subject to nonlocal conditions with self-adjoint operator". ed. T. E. Simos. Numerical Analysis and Applied Mathematics Icnaam 2011: International Conference on Numerical Analysis and Applied Mathematics, Vols A-C, AIP Conference Proceedings, 1389, 597-600.